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Answer:

k = +10 or -10

Step-by-step explanation:

It's given in the question that the roots of the eqn. are real and equal. So , the discriminant of the eqn. should be equal to 0.

[tex] = > {b}^{2} - 4ac = 0[/tex]

[tex] = > {( - 2k)}^{2} - 4 \times 5 \times 20 = 0[/tex]

[tex] = > 4 {k}^{2} - 400 = 0[/tex]

[tex] = > 4( {k}^{2} - 100) = 0[/tex]

[tex] = > {k}^{2} - 100 = 0[/tex]

[tex] = > k = \sqrt{100} = + 10 \: or \: - 10[/tex]

Step-by-step explanation:

Given Equation

5x-2kx+20=0

[tex]\boxed{\sf \longrightarrow D=0 }[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow b^2-4ac=0 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow (-2k)^2-4\times 5\times 20=0 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2-20\times 20=0 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2-400=0[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2=400 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k^2=\dfrac {400}{4}[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k^2=100 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k=\sqrt{100}[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k=10 [/tex]

[tex]\therefore\sf k=10 [/tex]

1. 7.2 x 100 =  720

2. 468.8 ÷ 100 =  4.688

3. 0.12 x 1,000 =  120

4. 86.4 ÷ 100 =  0.864

5. 2.001 x 10 =  20.01

6. 1,200 ÷ 1,000 =  1.2

7. 3.41 x 100 =  341

8. 3.41 ÷ 10 =  0.341

9. 0.0031 x 100 =  0.31

10. 5.7 ÷ 100 =  0.057

11. 1.34 x 1,000 =  1340

12. 10 x 0.57 =  5.7

13. 57 ÷ 100 =  0.57

14. 1.068 x 100 =  106.8

15. 168.1 ÷ 10 =  16.81

16. 0.0341 x 100 = 3.41

Answer:

3. Given: R is the midpoint of both PT and QS and TSR. ∆ are right triangles. Prove: PQR. ∆. ~ TSR. ∆. 5. Given: AB = CB = 9 cm.

Step-by-step explanation:

Δ PQR ≅ Δ TSR  by AAS congruency rule.

Two triangles are said to be congruent if their corresponding sides and angles are congruent to each other.

The given information are QR = SR and ∠ QPR = ∠ STR

The proof is as follows :-

             Statement                                                      Reasons

               QR = RS                                                          Given

           ∠ QPR = ∠ STR                                                  Given

           ∠ PRQ = ∠ TRS                                   Vertically opposite angles

            Δ PQR ≅ Δ TSR                                      AAS congruency rule

AAS congruency rule :-

Two triangles are said to be congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Hence, the triangles are congruent by AAS congruency rule.

For more references on congruency, click;

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Answer:

85.1 g

Step-by-step explanation:

Boris has 91.5 g of pepper

He used 0.4g to make one plate of scrambled egg

If she made 16 plates of scrambled egg then the amount of pepper that will be left can be calculated as follows

= 0.4×16

= 6.4g

= 91.5g - 6.4g

= 85.1g

Hence Boris will have 85.1g of pepper left

Answer:

C. The bagels at Store B are $0.04 more expensive than the bagels at Store A.

Step-by-step explanation:

Find the unit rates of both stores by dividing the price by the number of bagels:

Store A:

2.05/5

= 0.41

Store B:

1.35/3

= 0.45

Store B's bagels are $0.04 more than Store A's, so C is the correct answer.

Answer:

15ft

Step-by-step explanation:

Calculation for how tall is the tree

First step Let the proportion be x/10ft = 6ft /4ft

Second step is to cross-multiply by 4x

4x =10ft*6ft

4x = 60

Third step is to divide both sides by 4

4x = 60

4x/4=60/4

x=15 ft

Therefore the tree will be 15ft tall

Answer:

6.25 or 6 1/4

Step-by-step explanation:

Jodie sold 6.25 candy altogether.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that perform the arithmetic operations are called arithmetic operators.

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

For example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

Given that

Jodie sells 2½ pounds of gumdrops,

3 pounds of orange slices, and ¾ pounds of gummi bears.

Convert the fractions into decimals

Number of pounds of gumdrops = 2½ = 5/2 = 2.5

Number of pounds of gummi bears = ¾ = 0.75

So the total amount of candy Jodie sold :

⇒ 2.5 + 3 + 0.75

⇒ 6.25

Hence, Jodie sold 6.25 candy altogether.

Learn more about the fraction here:

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Answer:

1, -2

Step-by-step explanation:

The x axis is 1 to the right, and the y axis is 2 down.

Answer:

10 hours

Step-by-step explanation:

ok

7 / 8 i think correct me if im wrong!

Answer:

7/8

Step-by-step explanation:

PLEASE GIVE BRAINLIEST

It is because 7 times 1 is 7 and when multiplying a regular number by a fraction the denominator does not change.

Answer:

ok so the answer is b

Step-by-step explanation: because if you divide the numbers and you get the answer you will have to add and there is your answer and please give me a 5 star.

Answer:

I would say A

Step-by-step explanation:

Answer:

11 servings

Step-by-step explanation:

A recipe is 623 cups

1 serving is 56 cups

Now if 1 serving is 56 cups

x serving is 623 cups

x = 623/56

x= 11 servings

Answer:

Step-by-step explanation:

The terms will be multiplied in order to get the simplified polynomials.

a. 6(x + 7)(x + 2)

[tex]6(x + 7)(x + 2)\\=6[x(x+2)+7(x+2)]\\=6(x^2+2x+7x+14)\\=6(x^2+9x+14)\\=6x^2+54x+84[/tex]

The simplified form of 6(x + 7)(x + 2) is [tex]6x^2+54x+84[/tex]

b. (2y – 5)^2

Using the formula: [tex](a-b)^2 = a^2+b^2-2ab[/tex]

[tex]=(2y)^2+(5)^2-2(2y)(5)\\=4y^2+25-20y[/tex]

The simplified form is: [tex]4y^2-20y+25[/tex]

c. (5x + 4y)(2x - y)

[tex]=5x(2x-y)+4y(2x-y)\\=10x^2-5xy+8xy-4y^2\\=10x^2+3xy-4y^2[/tex]

The simplified form of (5x + 4y)(2x - y) is [tex]10x^2+3xy-4y^2[/tex]

d. (3x + 7)(3x – 7)

Using the formula: [tex](a+b)(a-b) = a^2-b^2[/tex]

[tex]= (3x)^2-(7)^2\\= 9x^2-49[/tex]

The simplified form of (3x + 7)(3x – 7) is [tex]9x^2-49[/tex]

e. (t + 2) – (4t +9) – t

[tex]=t+2-4t-9-t\\=t-4t-t+2-9\\= -4t-7[/tex]

The simplified form of (t + 2) – (4t +9) – t is [tex]-4t-7[/tex]

Hence,

a. The simplified form of 6(x + 7)(x + 2) is [tex]6x^2+54x+84[/tex]

b. The simplified form is: [tex]4y^2-20y+25[/tex]

c. The simplified form of (5x + 4y)(2x - y) is [tex]10x^2+3xy-4y^2[/tex]

d. The simplified form of (3x + 7)(3x – 7) is [tex]9x^2-49[/tex]

e. The simplified form of (t + 2) – (4t +9) – t is [tex]-4t-7[/tex]

Answer:

5 seconds

Step-by-step explanation:

Looking at your function (h(t) = -16t^2 + 48t + 160), I see that the peak height will be 196 feet, and that is achieved in 1.5 seconds.

h(1.5) = -16(1.5)^2 + 48(1.5) + 160

h(1.5) = -16(2.25)+ 48(1.5) + 160

h(1.5) = -36 + 48(1.5) + 160

h(1.5) = -36 + 72 + 160

h(1.5) = 36 + 160

h(1.5) = 196

Going down from that height, it would take 3.5 more seconds, so it would take 5 seconds in total

h(5) = -16(5)^2 + 48(5) + 160

h(5) = -16(25) + 48(5) + 160

h(5) = -400 + 48(5) + 160

h(5) = -400 + 240 + 160

h(5) = -400 + 400

h(5) = 0

Răspuns:

318 de participanți

Explicație pas cu pas:

Dat fiind:

Număr în parc = 106

Numărul din parc reprezintă 1/3 din numărul elevilor care participă la activitatea de curățenie.

Pentru a obține numărul total de studenți care participă la activitate; fie numărul total = x

Prin urmare;

1/3 din x = 106

x / 3 = 106

Înmulțiți ambele părți cu 3

x = 318

Prin urmare, numărul total de studenți implicați în activitatea de curățenie = 318 stuaen

Answer:

x=3

y=8

Step-by-step explanation:

the given equations are y=3x-1 --------(1)

and y=2x+2---------(2)

Using substitution method,

and solving y=3x-1

y+1=3x

or y+1/3 =x ------(3)

Putting the value of x= y + 1 / 3 in equation 2

y= 2x+2

or, y = 2 ( y + 1/3) +2

or, y= 2y + 2 / 3 +2

or, y = 2y + 2 + 6 // 3 ( Taking LCM)

Or, 3 y = 2y + 2 + 6 ( the denominator gets multiplied to y)

OR, 3 Y - 2Y =6 PLUS 2

or y = 8

therefore, y=8

now substituting the value of y=8 in equation (3)

y + 1 /3 = x

or ,,, 8 plus 1 by 3 =x

or,,,,, 9 by 3 =x

Therefore, x is 3

Answer:

reflection of ae

Step-by-step explanation:

b=a

e-d and it just flips

Answer:

The 80 p0und bag will last 128 days.

Step-by-step explanation:

In order to find out how much days the 80 pound bag last we have to divide the 80 pounds by the among that the dog eats each day. And so we get.....

80 / [tex]\frac{5}{8}[/tex] = [tex]\frac{80}{1} / \frac{5}{8}[/tex] = [tex](\frac{80}{1})(\frac{8}{5})[/tex] = [tex]\frac{640}{5}[/tex] = 128

Answer:

For some reason my answer got deleted.

The dog food will last 128 days,

Step-by-step explanation:

80 ÷ 5/8 = 128

Since 5/8 is being used each day, you divide.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

let H represent the head's outcome

let T represents the outcome of tails.

if the coin is tossed 3times The total number outcomes are

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

Answer:

Answer image is attached.

Step-by-step explanation:

Given rational expressions:

[tex]1.\ \dfrac{x^2+x+4}{x-2}\\2.\ \dfrac{x^2-x+4}{x-2}\\3.\ \dfrac{x^2-4x+10}{x-2}\\4.\ \dfrac{x^2-5x+16}{x-2}[/tex]

And the rewritten forms:

[tex](x-2)+\dfrac{6}{x-2}\\(x+3)+\dfrac{10}{x-2}\\(x+1)+\dfrac{6}{x-2}\\(x-3)+\dfrac{10}{x-2}[/tex]

We have to match the rewritten terms with the given expressions.

Let us consider the rewritten terms and let us solve them one by one by taking LCM.

[tex](x-2)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x-2)^{2}+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+4+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+10}{x-2}[/tex]

So, correct option is 3.

[tex](x+3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x+3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{(x^2+3x-2x-6)+10}{x-2}\\\Rightarrow \dfrac{x^2+x+4}{x-2}[/tex]

So, correct option is 1.

[tex](x+1)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x+1)(x-2)+6}{x-2}\\\Rightarrow \dfrac{x^{2} +x-2x-2+6}{x-2}\\\Rightarrow \dfrac{x^{2} -x+4}{x-2}[/tex]

So, correct option is 2.

[tex](x-3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x-3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{x^2-3x-2x+6+10}{x-2}\\\Rightarrow \dfrac{x^2-5x+16}{x-2}[/tex]

So, correct option is 4.

The answer is also attached in the answer area.

Answer:

I think is D

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

To make it shorter.

Answer:

{10,8}

Step-by-step explanation:

-3x + 4y = -62

4x + 5y = 0

let's eliminate the x

-3x + 4y = -62 | x -4 |

4x + 5y = 0 | x 3 |

12x - 16y = 248

12x + 15y = 0

-------------------- -

-31y = 248

y = 248/(-31) = 8

since you must do this proble with elimination, we cant use subtitution. so we repeat the way once more to find x (eliminate y)

-3x + 4y = -62 | x 5 |

4x + 5y = 0 | x 4 |

-15x + 20y = -310

16x + 20y = 0

-------------------- -

-31x = -310

x = -310/-31 = 10

Answer:

The correct is the little (B) 0.76